diff --git a/pkg/optimizer/hpoptimizer.go b/pkg/optimizer/hpoptimizer.go
index d2858e6e5..ea4494349 100644
--- a/pkg/optimizer/hpoptimizer.go
+++ b/pkg/optimizer/hpoptimizer.go
@@ -123,22 +123,46 @@ func (o *HyperparameterOptimizer) buildParamDomains() (map[string]string, []para
 		var domain paramDomain
 		switch selector.Type {
 		case selectorTypeRange, selectorTypeRangeFloat:
-			domain = &floatRangeDomain{
-				paramDomainBase: paramDomainBase{
-					label: selector.Label,
-					path:  selector.Path,
-				},
-				min: selector.Min.Float64(),
-				max: selector.Max.Float64(),
+			if selector.Step.IsZero() {
+				domain = &floatRangeDomain{
+					paramDomainBase: paramDomainBase{
+						label: selector.Label,
+						path:  selector.Path,
+					},
+					min: selector.Min.Float64(),
+					max: selector.Max.Float64(),
+				}
+			} else {
+				domain = &floatDiscreteRangeDomain{
+					paramDomainBase: paramDomainBase{
+						label: selector.Label,
+						path:  selector.Path,
+					},
+					min:  selector.Min.Float64(),
+					max:  selector.Max.Float64(),
+					step: selector.Step.Float64(),
+				}
 			}
 		case selectorTypeRangeInt:
-			domain = &intRangeDomain{
-				paramDomainBase: paramDomainBase{
-					label: selector.Label,
-					path:  selector.Path,
-				},
-				min: selector.Min.Int(),
-				max: selector.Max.Int(),
+			if selector.Step.IsZero() {
+				domain = &intRangeDomain{
+					paramDomainBase: paramDomainBase{
+						label: selector.Label,
+						path:  selector.Path,
+					},
+					min: selector.Min.Int(),
+					max: selector.Max.Int(),
+				}
+			} else {
+				domain = &intStepRangeDomain{
+					paramDomainBase: paramDomainBase{
+						label: selector.Label,
+						path:  selector.Path,
+					},
+					min:  selector.Min.Int(),
+					max:  selector.Max.Int(),
+					step: selector.Step.Int(),
+				}
 			}
 		case selectorTypeIterate, selectorTypeString:
 			domain = &stringDomain{
diff --git a/pkg/optimizer/hpoptimizer_test.go b/pkg/optimizer/hpoptimizer_test.go
index 490240f05..2107946b3 100644
--- a/pkg/optimizer/hpoptimizer_test.go
+++ b/pkg/optimizer/hpoptimizer_test.go
@@ -15,6 +15,15 @@ func TestBuildParamDomains(t *testing.T) {
 			max:             expect.Max.Float64(),
 		}
 	}
+	var floatDiscreteRangeDomainVerifier = func(domain paramDomain, expect SelectorConfig) bool {
+		concrete := domain.(*floatDiscreteRangeDomain)
+		return *concrete == floatDiscreteRangeDomain{
+			paramDomainBase: paramDomainBase{label: expect.Label, path: expect.Path},
+			min:             expect.Min.Float64(),
+			max:             expect.Max.Float64(),
+			step:            expect.Step.Float64(),
+		}
+	}
 	var intRangeDomainVerifier = func(domain paramDomain, expect SelectorConfig) bool {
 		concrete := domain.(*intRangeDomain)
 		return *concrete == intRangeDomain{
@@ -23,6 +32,15 @@ func TestBuildParamDomains(t *testing.T) {
 			max:             expect.Max.Int(),
 		}
 	}
+	var intStepRangeDomainVerifier = func(domain paramDomain, expect SelectorConfig) bool {
+		concrete := domain.(*intStepRangeDomain)
+		return *concrete == intStepRangeDomain{
+			paramDomainBase: paramDomainBase{label: expect.Label, path: expect.Path},
+			min:             expect.Min.Int(),
+			max:             expect.Max.Int(),
+			step:            expect.Step.Int(),
+		}
+	}
 	var stringDomainVerifier = func(domain paramDomain, expect SelectorConfig) bool {
 		concrete := domain.(*stringDomain)
 		expectBase := paramDomainBase{label: expect.Label, path: expect.Path}
@@ -56,8 +74,8 @@ func TestBuildParamDomains(t *testing.T) {
 				Label:  "range label",
 				Path:   "range path",
 				Values: []string{"ignore", "ignore"},
-				Min:    fixedpoint.NewFromFloat(0.0),
-				Max:    fixedpoint.NewFromFloat(0.0),
+				Min:    fixedpoint.NewFromFloat(7.0),
+				Max:    fixedpoint.NewFromFloat(80.0),
 				Step:   fixedpoint.NewFromFloat(0.0),
 			},
 			verify: floatRangeDomainVerifier,
@@ -67,11 +85,22 @@ func TestBuildParamDomains(t *testing.T) {
 				Label:  "rangeFloat label",
 				Path:   "rangeFloat path",
 				Values: []string{"ignore", "ignore"},
-				Min:    fixedpoint.NewFromFloat(0.0),
-				Max:    fixedpoint.NewFromFloat(0.0),
+				Min:    fixedpoint.NewFromFloat(6.0),
+				Max:    fixedpoint.NewFromFloat(10.0),
 				Step:   fixedpoint.NewFromFloat(0.0),
 			},
 			verify: floatRangeDomainVerifier,
+		}, {
+			config: SelectorConfig{
+				Type:   selectorTypeRangeFloat,
+				Label:  "rangeDiscreteFloat label",
+				Path:   "rangeDiscreteFloat path",
+				Values: []string{"ignore", "ignore"},
+				Min:    fixedpoint.NewFromFloat(6.0),
+				Max:    fixedpoint.NewFromFloat(10.0),
+				Step:   fixedpoint.NewFromFloat(2.0),
+			},
+			verify: floatDiscreteRangeDomainVerifier,
 		}, {
 			config: SelectorConfig{
 				Type:   selectorTypeRangeInt,
@@ -80,9 +109,20 @@ func TestBuildParamDomains(t *testing.T) {
 				Values: []string{"ignore", "ignore"},
 				Min:    fixedpoint.NewFromInt(3),
 				Max:    fixedpoint.NewFromInt(100),
-				Step:   fixedpoint.NewFromInt(66),
+				Step:   fixedpoint.NewFromInt(0),
 			},
 			verify: intRangeDomainVerifier,
+		}, {
+			config: SelectorConfig{
+				Type:   selectorTypeRangeInt,
+				Label:  "rangeInt label",
+				Path:   "rangeInt path",
+				Values: []string{"ignore", "ignore"},
+				Min:    fixedpoint.NewFromInt(3),
+				Max:    fixedpoint.NewFromInt(100),
+				Step:   fixedpoint.NewFromInt(7),
+			},
+			verify: intStepRangeDomainVerifier,
 		}, {
 			config: SelectorConfig{
 				Type:   selectorTypeIterate,
diff --git a/pkg/optimizer/hyperparam.go b/pkg/optimizer/hyperparam.go
index 31b699ea1..ae6222894 100644
--- a/pkg/optimizer/hyperparam.go
+++ b/pkg/optimizer/hyperparam.go
@@ -30,6 +30,22 @@ func (d *intRangeDomain) buildPatch(trial *goptuna.Trial) (jsonpatch.Patch, erro
 	return jsonpatch.DecodePatch(jsonOp)
 }
 
+type intStepRangeDomain struct {
+	paramDomainBase
+	min  int
+	max  int
+	step int
+}
+
+func (d *intStepRangeDomain) buildPatch(trial *goptuna.Trial) (jsonpatch.Patch, error) {
+	val, err := trial.SuggestStepInt(d.label, d.min, d.max, d.step)
+	if err != nil {
+		return nil, err
+	}
+	jsonOp := []byte(reformatJson(fmt.Sprintf(`[{"op": "replace", "path": "%s", "value": %v }]`, d.path, val)))
+	return jsonpatch.DecodePatch(jsonOp)
+}
+
 type floatRangeDomain struct {
 	paramDomainBase
 	min float64
@@ -45,6 +61,22 @@ func (d *floatRangeDomain) buildPatch(trial *goptuna.Trial) (jsonpatch.Patch, er
 	return jsonpatch.DecodePatch(jsonOp)
 }
 
+type floatDiscreteRangeDomain struct {
+	paramDomainBase
+	min  float64
+	max  float64
+	step float64
+}
+
+func (d *floatDiscreteRangeDomain) buildPatch(trial *goptuna.Trial) (jsonpatch.Patch, error) {
+	val, err := trial.SuggestDiscreteFloat(d.label, d.min, d.max, d.step)
+	if err != nil {
+		return nil, err
+	}
+	jsonOp := []byte(reformatJson(fmt.Sprintf(`[{"op": "replace", "path": "%s", "value": %v }]`, d.path, val)))
+	return jsonpatch.DecodePatch(jsonOp)
+}
+
 type stringDomain struct {
 	paramDomainBase
 	options []string